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Learning Math Home
Patterns, Functions, and Algebra
 
Session 3 Part A Part B Part C Part D Part E Homework
 
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Session 3 Materials:
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Solutions
 

A B C D E
Homework

Video

Solutions for Session 3, Part E

See solutions for Problems: E1 | E2 | E3 | E4 | E5 | E6 | E7 | E8 | E9 | E10 | E11
E12 | E13 | E14 | E15 | E16


Problem E1

In each case there are clear reasons that there can only be one answer. For example, a state can have only one capital city. A word can only have one first letter.

 

Integer

 

Odd or Even

1

 

odd

2

 

even

3

 

odd

4

 

even

5

 

odd

10

 

even

15

 

odd

 
 
 

SSN

 

DOB

590-14-6017

 

6/2/75

024-33-3467

 

10/27/70

024-33-3568

 

10/27/70

024-33-7146

 

8/10/74

036-89-0831

 

6/8/84

 

 

State

 

Capital

Massachusetts

 

Boston

Texas

 

Austin

Washington

 

Olympia

North Dakota

 

Bismarck

West Virginia

 

Charleston

 
 
 

Side Length

 

Area

1

 

1

2

 

4

3

 

9

4

 

16

5

 

25

10

 

100

15

 

225

 

 

Word

 

First Letter

Word

 

W

Hey

 

H

Wow

 

W

Math

 

M

Is

 

I

Very

 

V

Cool

 

C

 

<< back to Problem E1


 

Problem E2

Sure, but not always. The odd-or-even, date of birth, and letter functions have the possibility of matching outputs.

<< back to Problem E2


 

Problem E3

More tables!
For certain (not necessarily all!) inputs, there can be more than one correct output. Note how different this is from Algorithms A and B.

 

Number

 

Smaller Number

10

 

7

10

 

8

15

 

10

17

 

12

21

 

12

21

 

-5

0

 

-100

 
 
 

Number

 

Factor

15

 

3

20

 

5

24

 

3

24

 

4

30

 

10

45

 

9

100

 

20

 

 

Person

 

Grandparent

Abbey

 

Mary

Abbey

 

John

Megan

 

Mary

Megan

 

Alice

Brian

 

Henry

 
 
 

City Name

 

State Name

New York

 

New York

Chicago

 

Illinois

Salem

 

Massachusetts

Salem

 

Oregon

Portland

 

Oregon

Portland

 

Maine

 

 

Side Length

 

Area

5

 

20

10

 

20

20

 

20

1

 

1/4

5

 

15

10

 

50

100

 

250000

 
 
 

Word

 

Anagram

ear

 

are

ear

 

era

mare

 

ream

toilets

 

T. S. Eliot

relation

 

oriental

listen

 

silent

Elvis

 

lives

 

<< back to Problem E3


 

Problem E4

Other functions: a circle's circumference is a function of its radius; the average temperature is a function of the time of year; a TV program's rating is a function of the number of people watching the show. For each function, there can only be one output for a given input, while a non-function may have more than one output for the same input. For example, people of more than one age can wear size 11 shoes.

<< back to Problem E4


 

Problem E5

a. 

The output is yes, 3 is a prime number.

b. 

The output is yes, 2 is a prime number.

c. 

No, 100 is not a prime (it has lots of factors).

d. 

No, 1 is not a prime (it needs to have exactly two factors).

<< back to Problem E5


 

Problem E6

It could be any prime number: 2, 3, 5, 7, 11, 13, 17, 19, ... .

<< back to Problem E6


 

Problem E7

It's a function because there is exactly one output. The answer is always "yes" or "no," never both.

<< back to Problem E7


 

Problem E8

There is no such function. The outputs are only "yes" or "no," so if such a function existed, it would have to guarantee the specific prime number picked from "yes," which is impossible. Put another way, the undoing rule cannot be a function, because "yes" would return all the prime numbers, and "no" would return all the non-primes.

<< back to Problem E8


 

Problem E9

a. 

The output is 3.

b. 

The output is 3.

c. 

The output is still 3.

<< back to Problem E9


 

Problem E10

It could be any number at all. Since the output is always 3, telling us that the output is 3 doesn't give any new information. This is the same situation as Problem D5.

<< back to Problem E10


 

Problem E11

There is exactly one value for the output. It's always 3, but that doesn't keep it from being a function.

<< back to Problem E11


 

Problem E12

No such function exists.

<< back to Problem E12


 

Problem E13

The output is a triangle whose sides are 1/2 the sides of the original and parallel to the original sides.

<< back to Problem E13


 

Problem E14

All the sides are half as long, and the new triangle's area is one-fourth of the original.

<< back to Problem E14


 

Problem E15

All the formed quadrilaterals are parallelograms.

<< back to Problem E15


 

Problem E16

Yes, because there is exactly one output polygon for any starting polygon.

<< back to Problem E16


 

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